Growth annuity: elixir of sustainable growth?

ABSTRACT

This paper shows that growth annuity payment plans akin to graduated mortgage payments reduce the overall lending risk by alleviating the borrower's life-time likelihood of default particularly during the early years of the mortgage. This paper then argues that such lending practices not only reduces the overall default risk in the economy but also provides an alternative growth mechanism which is appealing to a much wider demography than traditional mortgage loans.

1. INTRODUCTION

While the prolonged recession of early 2000s has already taken its toll on the U.S. economy, the past socio-demographic growth policies are haunting a growing number of states. Most notable of these problems is the aging population and soaring Medicare and Medicade costs (see, e.g., Gavin (2000)). While throughout the booming 90s, many states, particularly the southeastern and southwestern states have taken steps to appease the rich "gray" America (see, e.g., American Demographics (2002)), more and more, these states are finding past actions problematic at best.

Since wealthy retirees frequently attempt to find second residences in warmer climates, state planners have devised "retiree-friendly" regulations to promote urban growth. While in a booming economy where market-generated incomes run high such policies seem quite successful, in a flat or stagnant economy these policies have started to burden states severely. Since most targeted demographics are at the downturn of their human capital, their consumption habits are rather conservative. As such, despite their handsome real estate investment, their ongoing contributions to the state economy, whether in form of income or sale tax, remain limited. However, by the natural necessity of aging process, this demographic demands ongoing medical and other related care, which for most part burdens the state tax income.

The inherent dilemma is thus produced by two conflicting factors: while the real estate growth requires more than median worth investors, the ongoing fiscal and economic health of the state demands growing tax revenues. In other words, while "gray" America supports the real estate boom, the younger generations fuel the economy. This in turn can and has caused clashes between the generations because it introduces wealth transfers. While the debate will undoubtedly continue over what policies may diminish the overall problem, we propose a simple solution which primarily focuses on the issues of real estate growth.

We conjecture that a growth annuity mortgage loan payment scheme can make expensive real estate more affordable to the younger generations and as such will provide states with the benefit of attracting the tax generating demographics. We also show that this is primarily achieved by reducing the default probability for lower income demographics which in turn can open huge untapped markets for realtors. Additionally, since such a lending scheme inherently has a lower default risk, the overall macroeconomic risk should further decline which in turn will help to sustain longer growth cycles.

2. ANALYSIS

As of December 2002, more than 34% of U.S. households earned between $45,000 to $100,000 per year (see, American Demographics (2002)). Given that the median housing price at the same time was in excess of $160,000 (Crist (2002)), this segment of the market remains largely shy of purchasing any prime, upper-end real estate property. Youthfulness comprises the majority of this segment of the market with heads of households ranging from 25 to 44 years of age, and is without questions the power engine of the economy.

To examine if our conjecture can help this segment of the market to access the prime real estate market, we simulate the income flow for individuals with three income profiles; low, median and high income, and then investigate which of two lending options, the conventional mortgage and growth annuity, provides more affordability. We define affordability as the likelihood of default.

To simulate the income, we assume that the individual's income follows a geometric Brownian motion as follows

(1) dC[F.sub.t] = [g.sub.inc] C[F.sub.t] + [sigma] C[F.sub.t] dB,

where [F.sub.t] is the income at time t, [g.sub.inc] is the person's income growth, [] is the volatility factor, and dB is a standard Brownian motion. To model the aforementioned process, we take 1000 draws from a standard normal distribution and then determine the person's income flow for ten years.

We assume that the property value is $200,000 and that the person should pay as down payment 15% of the value. All loans have a ten-year maturity and payments are payable at the end of the year. Table 1 shows the results of the simulations. The results verify our intuition that under a growth annuity scheme the default probability is lower. This is more apparent when the annuity's growth is more than income growth rate. Note that the payment flow for a growth annuity is given by:

(2) PMT = LOANx[[1/r(1-[[1+g/1+r].sup.N])].sup.1],

where r is the mortgage rate, g is the mortgage growth rate, and N is the maturity. Note that the payment for conventional mortgage can be defined by (2) by enforcing g to be zero.

For simplicity in our analysis, we assume that mortgage growth rate is equal to average inflation rate of 3%. Note that as long as the income growth rate is more than mortgage growth rate, the default probability decreases over time. It is only when income growth is lower than mortgage growth that the default probability increases as time progresses. This is quite intuitive because while costs are rising at a fast pace, the income flow is barely catching up.

We further investigate the relative affordability of the two lending schemes by contrasting the minimum annual income required to support either loans. Figure 1 provides a comparison of the two loan types. Clearly, the growth annuity scheme provides better affordability in the sense that as the mortgage growth rate rises, the minimum income drops precipitately. Note that here we assume that both income growth rate and mortgage are the same.

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3. CONCLUSION

We argue that growth annuity payment type loans, similar to a graduated mortgage, can reduce the overall default risk of mortgage lending and increase the affordability of real estate lending. This is turn can open prime real estate markets to a large untapped middle-income class which cannot otherwise afford high priced housing. States that promote such lending practices can in turn attract a younger and more economically vital demographic to their region who will then provide the local economy with an array of benefits, among which is their long-term tax generating potential.

FIGURE 1 Mortgage Affordability

This figure shows the minimum annual income required to receive the loan. The minimum income is defined as four times the first mortgage payment. While this exaggerates the growth annuity affordability, it does provide a visual sense of how the two loan types compare with each other. Here, we assume that the individual undertakes a ten-year $200,000 loan with 15% down payment rate. Both income and mortgage growth rates are assumed to be equal. Mortgage rate is 5% or 8%.

TABLE 1
Default Probabilities of Conventional Mortgage and Growth Annuity

This table compares the success probabilities of conventional
mortgage and growth annuity for three types of borrowers: low
income with an annual salary of $50,000, median income with an
annual salary of $100,000 and high income with a salary of
$150,000. The initial property value is assumed to be $200,000
and down payment is set to be 85%. The current mortgage rate is
8% for all borrowers. The loan has a 10-year maturity with annual
payments, which are made at the end of each year. The income growth
rate is exogenous of inflation rate. Growth annuity is assumed to
be growing at the inflation rate of 3%.

     Low Income        Median Income     High Income

     Pr   [Pr.sub.g]   Pr   [Pr.sub.g]   Pr   [Pr.sub.g]
Year

Panel A. [g.sub.inc] = 3%

1    81   87           92   98           98   99
2    81   87           92   98           98   99
3    82   87           93   98           99   99
4    84   87           94   98           99   99
5    85   87           95   98           99   99
6    85   87           95   98           99   99
7    87   87           98   98           99   99
8    87   87           98   98           99   99
9    87   87           98   98           99   99
10   87   87           98   98           99   99

Panel B. [g.sub.inc] = 5%

1    87   89           98   98           99   99
2    87   89           98   98           99   99
3    89   90           98   99           99   99
4    89   90           98   99           99   99
5    89   90           98   99           99   99
6    90   90           99   99           99   99
7    90   90           99   99           99   99
8    91   91           99   99           99   99
9    91   91           99   99           99   99
10   92   91           99   99           99   99

Panel C. [g.sub.inc] = 1%

1    74   80           90   91           96   98
2    74   80           90   91           97   98
3    74   79           90   91           98   98
4    74   79           90   91           98   98
5    75   79           90   91           98   98
6    76   78           90   90           98   98
7    78   78           90   90           98   98
8    78   75           90   90           98   98
9    78   74           90   90           98   98
10   78   74           91   90           98   96

4. REFERENCES

Gavin, Robert, "Rising Health-Care Costs Escape Politicians' Notice", Wall Street Journal, New York, Aug 9, 2000.

Crist, Dean, "Housing Activity", Housing Economics, Washington, Vol. 50, (4), 2002, 21-23.

Anonymous, "Income Report", American Demographics, Ithaca, Vol. 24, (11), 2002, 36-38.

Dr. All Nejadmalayeri earned a Ph.D. at the University of Arizona in 2001. Currently he is an assistant professor of finance at the University of Nevada, Reno.

Ms. Caroline Patrick earned a M.A. at Utah State University in 1993. Currently she is the Director of International Initiatives at the Eller College of Business and Public Administration, at the University of Arizona.